Hetware wrote:>quasi wrote:>>>>On the other hand, suppose your proposed question is reworded>>in the following way ...>>>>Given:>>>> f(x) is defined and continuous for all x in R.>>I believe we can drop the "defined" since it is implied>by "continuous".

Yes.

>>Then if g is defined by>>>> g(x) = limit (s -> x) f(s)>>>>can g(x) be used to determine the value of f(x) for all x in R?>>>>The answer is yes -- in fact, f(x) = g(x) for all x in R.>>What is your opinion of the definition given as follows:>>Let f(x) be continuous over R, and f(x) = x/x for all x in R>where x/x is a determinate form?

I wouldn't use the phrase:

"where x/x is a determinate form"

Instead say:

"where x/x is defined"

You could also say it more simply this way:

"Let f be a function which is continuous over R and such that f(x) = x/x for x != 0."

Or even simpler:

"Let f(x) = 1.

But at this point, you surely understand the terminology andconventions relating to this issue as used in the text byThomas. Why not just go on from there?